Abstract

All-optical multistage interconnection networks are desirable for overcoming the limitations of optical signal regeneration in switching systems. We present a new implementation of the perfect-shuffle interconnection pattern that is coupled with an all-optical switching element, forming a complete stage of a multistage network. Switching is performed with birefringent calcite crystals and a ferroelectric liquid-crystal device, while interconnection is achieved with a space-semivariant imaging configuration. Cascading the layout allows this system to be used to construct an all-optical multistage interconnection network. An experimental demonstration of the stage is presented.

© 1998 Optical Society of America

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References

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  1. C.-L. Wu, T.-Y. Feng, “The universality of the shuffle–exchange network,” IEEE Trans. Comput. C-30, 324–331 (1981).
    [CrossRef]
  2. H. S. Stone, “Parallel processing with the perfect shuffle,” IEEE Trans. Comput. C-20, 153–161 (1971).
    [CrossRef]
  3. C.-L. Wu, T.-Y. Feng, “On a class of multistage interconnection networks,” IEEE Trans. Comput. C-29, 694–702 (1980).
    [CrossRef]
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    [CrossRef] [PubMed]
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1997 (2)

1996 (1)

1995 (1)

1994 (1)

1991 (1)

T. C. Chieu, J. L. Sanford, K.-H. Yang, “A high-resolution and high-speed ferroelectric liquid-crystal shutter array print head,” IEEE Trans. Electron. Dev. 38, 1316–1323 (1991).
[CrossRef]

1988 (2)

1986 (1)

1981 (1)

C.-L. Wu, T.-Y. Feng, “The universality of the shuffle–exchange network,” IEEE Trans. Comput. C-30, 324–331 (1981).
[CrossRef]

1980 (3)

1971 (1)

H. S. Stone, “Parallel processing with the perfect shuffle,” IEEE Trans. Comput. C-20, 153–161 (1971).
[CrossRef]

Brenner, K.-H.

Cheng, J.

Chieu, T. C.

T. C. Chieu, J. L. Sanford, K.-H. Yang, “A high-resolution and high-speed ferroelectric liquid-crystal shutter array print head,” IEEE Trans. Electron. Dev. 38, 1316–1323 (1991).
[CrossRef]

Fainman, Y.

Feng, T.-Y.

C.-L. Wu, T.-Y. Feng, “The universality of the shuffle–exchange network,” IEEE Trans. Comput. C-30, 324–331 (1981).
[CrossRef]

C.-L. Wu, T.-Y. Feng, “On a class of multistage interconnection networks,” IEEE Trans. Comput. C-29, 694–702 (1980).
[CrossRef]

Ford, J. E.

Glaser, I.

A. A. Sawchuk, I. Glaser, “Geometries for optical implementation of the perfect shuffle,” in Optical Computing 1988, J. W. Goodman, P. Chavel, G. Roblin, eds., Proc. SPIE963, 270–279 (1988).

Huang, A.

Krishnamoorthy, A. V.

Lee, S. H.

Li, Y.

Liu, L.

Lohmann, A. W.

Marchand, P.

Marom, D. M.

McMahon, D. H.

Mendlovic, D.

Sanford, J. L.

T. C. Chieu, J. L. Sanford, K.-H. Yang, “A high-resolution and high-speed ferroelectric liquid-crystal shutter array print head,” IEEE Trans. Electron. Dev. 38, 1316–1323 (1991).
[CrossRef]

Sauer, F.

Sawchuk, A. A.

A. A. Sawchuk, I. Glaser, “Geometries for optical implementation of the perfect shuffle,” in Optical Computing 1988, J. W. Goodman, P. Chavel, G. Roblin, eds., Proc. SPIE963, 270–279 (1988).

Soref, R. A.

Stone, H. S.

H. S. Stone, “Parallel processing with the perfect shuffle,” IEEE Trans. Comput. C-20, 153–161 (1971).
[CrossRef]

Stork, W.

Stücke, G.

Urquhart, K. S.

Wagner, R. E.

Wang, N.

Wu, C.-L.

C.-L. Wu, T.-Y. Feng, “The universality of the shuffle–exchange network,” IEEE Trans. Comput. C-30, 324–331 (1981).
[CrossRef]

C.-L. Wu, T.-Y. Feng, “On a class of multistage interconnection networks,” IEEE Trans. Comput. C-29, 694–702 (1980).
[CrossRef]

Xu, F.

Yang, K.-H.

T. C. Chieu, J. L. Sanford, K.-H. Yang, “A high-resolution and high-speed ferroelectric liquid-crystal shutter array print head,” IEEE Trans. Electron. Dev. 38, 1316–1323 (1991).
[CrossRef]

Yin, Y.

Appl. Opt. (9)

IEEE Trans. Comput. (3)

C.-L. Wu, T.-Y. Feng, “The universality of the shuffle–exchange network,” IEEE Trans. Comput. C-30, 324–331 (1981).
[CrossRef]

H. S. Stone, “Parallel processing with the perfect shuffle,” IEEE Trans. Comput. C-20, 153–161 (1971).
[CrossRef]

C.-L. Wu, T.-Y. Feng, “On a class of multistage interconnection networks,” IEEE Trans. Comput. C-29, 694–702 (1980).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

T. C. Chieu, J. L. Sanford, K.-H. Yang, “A high-resolution and high-speed ferroelectric liquid-crystal shutter array print head,” IEEE Trans. Electron. Dev. 38, 1316–1323 (1991).
[CrossRef]

Opt. Lett. (1)

Other (1)

A. A. Sawchuk, I. Glaser, “Geometries for optical implementation of the perfect shuffle,” in Optical Computing 1988, J. W. Goodman, P. Chavel, G. Roblin, eds., Proc. SPIE963, 270–279 (1988).

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Figures (4)

Fig. 1
Fig. 1

Omega network for interconnecting eight channels composed of three identical stages each with a perfect-shuffle permutation and four bypass–exchange switches (represented by the rectangular boxes).

Fig. 2
Fig. 2

Optical setup of the bypass–exchange switch. The calcite crystals serve to combine or split two orthogonally polarized beams. A FLC device is used as a controllable half-wave plate to rotate the polarization of both signals.

Fig. 3
Fig. 3

Optical setup for a complete stage of an Omega network, as described in Section 3. The output signals’ locations might vary according to the switch settings.

Fig. 4
Fig. 4

Experimental images obtained at various locations in the stage: (a) in the input vector, (b) after the modified perfect-shuffle imaging optics and reduction of the signal size by a mask, and (c) after the combination of vertical pairs by the first calcite crystal. Also shown is the output vector at different switch settings: (d) all switches in the bypass mode and (e) on all switches in the exchange mode. Note that the signal labels were added with photoediting software (no further editing was performed).

Equations (2)

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k 2 k if   0   k N / 2 - 1 2 k - N + 1 if   N / 2 k N - 1 ,
k - Δ y / 2 ,   2 k if   0 k N / 2 - 1 Δ y / 2 ,   2 k - N if   N / 2 k N - 1 ,

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